Related papers: Scattering with Neural Operators
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For…
Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasi-energy which is…
Transfer operators have been used widely to study the long time properties of chaotic maps or flows. We describe quantum analogues of these operators, which have been used as toy models by the quantum chaos community, but are also relevant…
Deep neural networks have rightfully won the place of one of the most accurate analysis tools in high energy physics. In this paper we will cover several methods of improving the performance of a deep neural network in a classification task…
We develop a physics-informed neural networks (PINNs) framework for the inverse scattering problem in nuclear physics and apply it to the $P_{3/2}$ partial wave of neutron-alpha elastic scattering. The radial potential is represented by a…
This article presents an approach to the two-dimensional Schr\"odinger equation based on automatic learning methods with neural networks. It is intended to determine the ground state of a particle confined in any two-dimensional potential,…
We study the scattering properties of Schr\"{o}dinger operators with bounded potentials concentrated near a subspace of $\mathbb{R}^d$. For such operators, we show the existence of scattering states and characterize their orthogonal…
The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts…
Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier…
Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…
In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at…
Accurate numerical solutions for the Schr\"odinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining…
A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh-Weyl $m$-function is proved. This result is applied to scattering…
We investigate multiple scattering of scalar waves by an ensemble of $N$ resonant point scatterers in three dimensions. For up to $N = 21$ scatterers, we numerically optimize the positions of the individual scatterers, such as to maximize…
Let $M$ be a scattering manifold, i.e., a Riemannian manifold with asymptotically conic structure, and let $H$ be a Schr\"odinger operator on $M$. We can construct a natural time-dependent scattering theory for $H$ with a suitable reference…
We develop direct scattering theory for one-dimensional Schr\"odinger operators with steplike potentials, which are asymptotically close to different Bohr almost periodic infinite-gap potentials on different half-axes.
For challenging state estimation problems arising in domains like vision and robotics, particle-based representations attractively enable temporal reasoning about multiple posterior modes. Particle smoothers offer the potential for more…
Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is…